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3 years ago

The following graph shows a system of inequalities.

Mathematics

1 answer:

ANTONII [103]3 years ago

5 0

Answer:

Yes, the point is a solution.

Step-by-step explanation:

A system of inequalities displayed on a graph has two shaded regions, and for this example, one is red and the other is blue. The region that contains all the solutions to the system of inequalities is where the two regions intersect to usually form a new color, which in this case is purple. We can see that the point (2,2) is located within the purple region, so therefore, yes, the point is a solution.

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How many 1/8-inch pieces of ribbon can be cut from a piece of ribbon that is 3/4 inch long? It can't be a fraction, sadly :')

SIZIF [17.4K]

Answer:

6 pieces.

Step-by-step explanation:

3/4 divided by 1/8

= 3/4 / 1/8

Invert the 1/8 and multiply:

= 3/4 * 8/1

= 24/4

= 6.

7 0

3 years ago

Read 2 more answers

If we inscribe a circle such that it is touching all six corners of a regular hexagon of side 10 inches, what is the area of the

Brrunno [24]

Answer:

$\left(100\pi - 150\sqrt{3}\right)$ square inches.

Step-by-step explanation:

<h3>Area of the Inscribed Hexagon</h3>

Refer to the first diagram attached. This inscribed regular hexagon can be split into six equilateral triangles. The length of each side of these triangle will be $10$ inches (same as the length of each side of the regular hexagon.)

Refer to the second attachment for one of these equilateral triangles.

Let segment $\sf CH$ be a height on side $\sf AB$ . Since this triangle is equilateral, the size of each internal angle will be $\sf 60^\circ$ . The length of segment

$\displaystyle 10\, \sin\left(60^\circ\right) = 10 \times \frac{\sqrt{3}}{2} = 5\sqrt{3}$ .

The area (in square inches) of this equilateral triangle will be:

$\begin{aligned}&\frac{1}{2} \times \text{Base} \times\text{Height} \\ &= \frac{1}{2} \times 10 \times 5\sqrt{3}= 25\sqrt{3} \end{aligned}$ .

Note that the inscribed hexagon in this question is made up of six equilateral triangles like this one. Therefore, the area (in square inches) of this hexagon will be:

$\displaystyle 6 \times 25\sqrt{3} = 150\sqrt{3}$ .

<h3>Area of of the circle that is not covered</h3>

Refer to the first diagram. The length of each side of these equilateral triangles is the same as the radius of the circle. Since the length of one such side is $10$ inches, the radius of this circle will also be $10$ inches.

The area (in square inches) of a circle of radius $10$ inches is:

$\pi \times (\text{radius})^2 = \pi \times 10^2 = 100\pi$ .

The area (in square inches) of the circle that the hexagon did not cover would be:

$\begin{aligned}&\text{Area of circle} - \text{Area of hexagon} \\ &= 100\pi - 150\sqrt{3}\end{aligned}$ .

3 0

3 years ago

When y=_7, find the value of 2y2- 9

topjm [15]

2x(-7)^2-9 = 2x49-9=98-9=89 maybe

7 0

3 years ago

Given that y= 12 cm and θ= 24 °, work out x rounded to 1 DP.<br><br> (not drawn to scale.)

padilas [110]

Answer:

$\huge\boxed{\sf x = 5.3}$

Step-by-step explanation:

<h3><u>Given:</u></h3>

y = 12 cm

θ = 24°

Using trigonometric ratio, tan.

$\displaystyle \boxed{tan \theta = \frac{opposite}{adjacent} }\\\\tan \ 24 = \frac{x}{12} \\\\0.445 = \frac{x}{12} \\\\Multiply \ 12 \ to \ both \ sides\\\\0.445 \times 12 = x\\\\5.3 = x\\\\x = 5.3\\\\\rule[225]{225}{2}$

5 0

2 years ago

Solve each equation and check.show all work.

harina [27]

Answer:

-b=11

Step-by-step explanation:

Nothing else is equal to a number except its self

4 0

3 years ago